Question

The length of a rectangle is 3 centimeters less than its width. What are the dimensions of the rectangle if its area is 108 square​ centimeters?

Answer 1

Width: `12" cm." color(white)("XXX")`Length: `9" cm."`

Explanation:

Let the width be `W` cm. and the length be `L` cm.

We are told
`color(white)("XXX")L=W-3`
and
`color(white)("XXX")"Area" = 108 "cm"^2`

Since `"Area"= LxxW`

`color(white)("XXX")LxxW=108`

`color(white)("XXX")(W-3)xxW=108`

`color(white)("XXX")W^2-3W-108=0`

`color(white)("XXX")(W-12)(W+9)=0`

So
#{: ("either",(W-12)=0," or ",(W+9)=0), (,rarr W=12,,rarrW=-9), (,,,"Impossible since distance must be " > 0) :}#

Therefore
`color(white)("XXX")W=12`
and
since `L=W-3`
`color(white)("XXX")L=9`